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An algebraist’s view on border bases

An algebraist’s view on border bases,10.1007/3-540-27357-3_4,Achim Kehrein,Martin Kreuzer,Lorenzo Robbiano

An algebraist’s view on border bases   (Citations: 21)
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This chapter is devoted to laying the algebraic foundations for border bases of ideals. Using an order ideal O\mathcal{O}, we describe a zero-dimensional ideal from the outside. The first and higher borders of O\mathcal{O} can be used to measure the distance of a term from O\mathcal{O} and to define O\mathcal{O}-border bases. We study their existence and uniqueness, their relation to Gröbner bases, and their characterization in terms of commuting matrices. Finally, we use border bases to solve a problem coming from statistics.
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